


from __future__ import annotations

from random import random






class _lowerCamelCase:
       def __init__(   self, lowerCamelCase = None)			->  Optional[Any]:




           """simple docstring"""

           _lowercase			:				Dict 						=						value
           _lowercase			:				Dict 						=						random()
           _lowercase			:				Node | None 						=						None
           _lowercase			:				Node | None 						=						None
       def __repr__(   self)			->  str:




           """simple docstring"""

           from pprint import pformat

           if self.left is None and self.right is None:
               return F'''\'{self.value}: {self.prior:.5}\''''
           else:
               return pformat(
                   {F'''{self.value}: {self.prior:.5}''': (self.left, self.right)}, indent=1)




       def __str__(   self)			->  str:




           """simple docstring"""

           _lowercase			:				List[str] 						=						str(self.value) + ' '
           _lowercase			:				Dict 						=						str(self.left or '')
           _lowercase			:				str 						=						str(self.right or '')
           return value + left + right



def 							UpperCamelCase_( lowerCamelCase_				,					lowerCamelCase_					)       ->		tuple[Node | None, Node | None]:
    if root is None:  # None tree is split into 2 Nones
        return None, None
    elif root.value is None:
        return None, None
    else:
        if value < root.value:
            _lowercase						,							_lowercase			:				List[str] 						=						split(root.left				,					lowerCamelCase_					)
            return left, root
        else:
            _lowercase						,							_lowercase			:				str 						=						split(root.right				,					lowerCamelCase_					)
            return root, right



def 							UpperCamelCase_( lowerCamelCase_				,					lowerCamelCase_					)       ->		Node | None:
    if (not left) or (not right):  # If one node is None, return the other
        return left or right
    elif left.prior < right.prior:
        _lowercase			:				List[str] 						=						merge(left.right				,					lowerCamelCase_					)
        return left
    else:
        _lowercase			:				Dict 						=						merge(lowerCamelCase_				,					right.left					)
        return right



def 							UpperCamelCase_( lowerCamelCase_				,					lowerCamelCase_					)       ->		Node | None:
    _lowercase			:				Optional[int] 						=						Node(lowerCamelCase_					)
    _lowercase						,							_lowercase			:				Optional[int] 						=						split(lowerCamelCase_				,					lowerCamelCase_					)
    return merge(merge(lowerCamelCase_				,					lowerCamelCase_					)				,					lowerCamelCase_					)



def 							UpperCamelCase_( lowerCamelCase_				,					lowerCamelCase_					)       ->		Node | None:
    _lowercase						,							_lowercase			:				Tuple 						=						split(lowerCamelCase_				,					value - 1					)
    _lowercase						,							_lowercase			:				Union[str, Any] 						=						split(lowerCamelCase_				,					lowerCamelCase_					)
    return merge(lowerCamelCase_				,					lowerCamelCase_					)



def 							UpperCamelCase_( lowerCamelCase_					)       ->		None:
    if not root:  # None
        return
    else:
        inorder(root.left					)
        print(root.value				,					end=','					)
        inorder(root.right					)



def 							UpperCamelCase_( lowerCamelCase_				,					lowerCamelCase_					)       ->		Node | None:
    for arg in args.split():
        if arg[0] == "+":
            _lowercase			:				Optional[Any] 						=						insert(lowerCamelCase_				,					int(arg[1:]					)					)

        elif arg[0] == "-":
            _lowercase			:				List[str] 						=						erase(lowerCamelCase_				,					int(arg[1:]					)					)

        else:
            print('Unknown command'					)

    return root



def 							UpperCamelCase_( )       ->		None:
    _lowercase			:				List[str] 						=						None
    print(
        'enter numbers to create a tree, + value to add value into treap, '
        '- value to erase all nodes with value. \'q\' to quit. '					)

    _lowercase			:				Union[str, Any] 						=						input()
    while args != "q":
        _lowercase			:				int 						=						interact_treap(lowerCamelCase_				,					lowerCamelCase_					)
        print(lowerCamelCase_					)
        _lowercase			:				Optional[int] 						=						input()

    print('good by!'					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()



'''simple docstring'''




def __lowerCAmelCase					(				UpperCamelCase__							)      ->       float:
    __lowerCamelCase            =    0
    while len(UpperCamelCase__							) > 1:
        __lowerCamelCase            =    0
        # Consider two files with minimum cost to be merged
        for _ in range(2							):
            __lowerCamelCase            =    files.index(min(UpperCamelCase__							)							)
            temp += files[min_index]
            files.pop(UpperCamelCase__							)
        files.append(UpperCamelCase__							)
        optimal_merge_cost += temp
    return optimal_merge_cost


if __name__ == "__main__":
  import doctest

  doctest.testmod()
